"Never again will we allow police to fire live bullets on demonstrators, students or others in DR Congo," Aubin Minaku, the speaker of the country's National Assembly, said in a tweet.
"There was a lapse, no supposed authority can give an order to fire on its people," he said.
According to rights groups, at least 40 people have died in protests over the past week against a proposed bill that could extend Kabila's hold on power in the vast African nation.
In a statement today, Human Rights Watch said that security forces used excessive force during the protests and then tried to remove evidence.
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It said it has confirmed 36 dead in protests in the capital Kinshasa, 21 of whom were fatally shot by security forces, and four dead in the eastern city of Goma.
A previous toll by the International Federation of Human Rights (FIDH) put the toll at 42.
The demonstrations broke out after the National Assembly last weekend passed a contested bill that many see as an attempt by Kabila to stay in power.
If lawmakers cannot come to an agreement, the National Assembly would have the final word.
At issue in the contested bill is a provision that ties 2016 presidential and legislative elections to a census, which is supposed to begin this year and is expected to take up to three years to complete.
Opponents of Kabila, who is constitutionally mandated to step down in 2016 when his second term ends, say he is trying to cling to power.
Kabila, now 43, came to power in January 2001 when politicians rushed to make the young soldier head of state after the assassination of his father, rebel-turned-president Laurent Kabila.